The present invention relates to digital signal processing, and more particularly in one embodiment, to selection of filter coefficients.
In any practical implementation of digital filters, the filter coefficients must be coded on finite length words. As is well known, rounding the coefficients to the nearest available value can deteriorate significantly the filter""s response, and it is rarely easy to find an optimal quantized filter.
Quantizing the filter coefficients to N bits introduces an error component which is responsible for the deterioration of the filter""s frequency response. Depending on whether rounding or truncating is used, the error component has a maximum amplitude (in time) of half a LSB or one LSB and its undesirable effect is only seen in the stop-band, where the response of the ideal filter is very low and does not mask the error response.
Unfortunately, the error component often severely undermines the efforts put into filter design, by altering the attenuation in the stop-band. Standard ways of coping with this problem include iterative filter design techniques where the design procedure is performed directly in the quantized domain, and exhaustive search for optimal rounding selection.
Iterative filter design techniques usually yield good results, but are computationally expensive, which prohibits their use in real-time applications. Moreover, the techniques tend to be complex and sensitive to initial conditions.
Exhaustive search implies the design of an optimal, non-quantized filter, followed by an exhaustive search, for each coefficient of the optimal quantized value. This approach guarantees a global optimum within the search range, but becomes impractical for filter length above about 20 coefficients, since the number of combinations to test is 2L where L is the number of filter coefficients when rounding towards ∞ of xe2x88x92∞ is tested, i.e., taking the integer number immediately below and taking the integer number immediately above, respectively.
What is needed is a computationally efficient technique for selecting quantized filter coefficients that will provide a desired filter response.
Improved methods and systems for generating quantized filter coefficients for a desired filter response are provided by virtue of the present invention. In one embodiment, a technique is provided to quantize the coefficients of finite impulse-response filters in a way that results in better performance than would be possible using simple truncation or rounding. The technique can be applied, e.g., to highpass, lowpass, or bandpass filters.
In one embodiment, the technique provides a mathematically sub-optimal solution which involves frequency-domain noise-shaping of the quantization error. The quantization error component is moved into a frequency region where it will be harmless, by reducing the impact of the quantization error component in the frequency region where it could be harmful. Considering a highpass filter, for example, one will try to reject most of the quantization error into the high-frequency region where it will be masked by the filter""s response, and minimize the error in the low-frequency region to preserve the quality of the stop-band.
A further understanding of the nature and advantages of the inventions herein may be realized by reference to the remaining portions of the specification and the attached drawings.